Question

Exact value of (sin30°)(tan45°)+(tan30°)(sin60°)=

Answer 1

(sin 30°)(tan 45°) + (tan 30°)(sin 60°) = 1

Given :

(sin 30°)(tan 45°) + (tan 30°)(sin 60°)

To find :

Exact value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(sin 30°)(tan 45°) + (tan 30°)(sin 60°)

Step 2 of 2 :

Find the value of the expression

(sin 30°)(tan 45°) + (tan 30°)(sin 60°)

$\displaystyle \sf = \bigg(\frac{1}{2} \times 1 \bigg)+ \bigg( \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{2} \bigg)$

$\displaystyle \sf = \frac{1}{2} + \frac{1}{2}$

$\displaystyle \sf = \frac{1 + 1}{2}$

$\displaystyle \sf = \frac{2}{2}$

$\displaystyle \sf = 1$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ if x cos a=8 and 15cosec a=8sec a then the value of x is

https://brainly.in/question/46325503

2. 7 cos 30° + 5 tan 30° + 6 cot 60° is

https://brainly.in/question/46167849

3. 1+ sin2α = 3 sinα cosα, then values of cot α are

https://brainly.in/question/46265791

Answer 2

Concept:

Sine(x), Cos(x), and Tan(x) are the trigonometric functions. These functions are generally a ratio of the sides present in a right-angle triangle. Sin(x) is the ratio of the opposite side of the angle x to that of Hypotenuses. Similarly, Cos(x) governs the ratio of the adjacent side of angle x to that of Hypotenuses. And finally, Tan(x) is the ratio of Sin(x) to Cos (x).

They have a standard value for any given value.

Given Equation:

(sin30°)(tan45°)+(tan30°)(sin60°)......(1)

Find:

The solution/RHS of equation 1

Standard Values:

sin 30° = 1/2 = 0.5

tan 45° = 1

tan 30° = 1/√3 = 0.575

sin 60° = √3/2 = 0.866

Putting all the values in equation 1,

(sin30°)(tan45°)+(tan30°)(sin60°)=?

(0.5*1) + (0.575*0.866)

= 0.5 + 0.5

=1

Or.

By taking the fractions:

$\frac{1}{2} * 1 + (\frac{1}{\sqrt{3} } * \frac{\sqrt{3} }{2} )$

$\frac{1}{2} + \frac{1}{2}$

= 1

Hence, The value of (sin30°)(tan45°)+(tan30°)(sin60°) = 1

#SPJ3